January 11, 2011 8:58 WSPC/S0219-6220 173-IJITDM …icserv.gist.ac.kr/mis/publications/data/2011/S... · · 2011-01-19January 11, 2011 8:58 WSPC/S0219-6220 173-IJITDM 00424 International

January 11, 2011 8:58 WSPC/S0219-6220 173-IJITDM 00424

International Journal of Information Technology & Decision MakingVol. 10, No. 1 (2011) 109–120c© World Scientific Publishing CompanyDOI: 10.1142/S0219622011004245

MULTIPLE-CRITERIA DECISION-MAKINGBASED ON PROBABILISTIC ESTIMATION

WITH CONTEXTUAL INFORMATIONFOR PHYSIOLOGICAL SIGNAL MONITORING

AHYOUNG CHOI∗ and WOONTACK WOO†

School of Information and MechatronicsGwangju Institute of Science and Technology

Gwangju, 500-712, South Korea∗[email protected]†[email protected]

We propose a multiple-criteria decision-making (MCDM) method based on MaximumA Posteriori (MAP) estimation to analyze users’ physiological status either normal orabnormal. The decision-making problem is formulated using MAP estimation and isturned out to be MCDM problem given the assumption that all probability densityfunctions (pdfs) follow exponential forms, especially Gaussian. It indicates that this

MCDM equation is decomposed into direct sum of group’s physiological status distribu-tion. Group distribution is estimated by probabilistic approach using population fromthe same age or same sex. For verification, we applied the proposed method to publicheart rate database. According to experimental results, the proposed method consid-ering group context reduced overall classification errors by 20.42% compared to typi-cal decision-making (TDM) method. This method is applicable to various personalizedhealth monitoring applications, which estimates user’s physiological status by referringother group distribution without prior knowledge about previous health records.

Keywords: Multiple-criteria decision-making; probabilistic decision-making; groupcontext; physiological signal monitoring.

1. Introduction

The advent of lightweight and high performing hardware technology acceleratesthe development of physiological monitoring systems.1–3 Typical decision-making(TDM) methods in these systems indicate users’ physiological status whether theyare under normal physiological condition or not, based on statistical analysis (mean,standard deviation, etc.) from a large data set. However, TDM methods cannotguarantee the reliable classification of all types of users, e.g. people with abnormallyhigh heart rate during rests. Thus, the best way to accurately estimate physiologicalstates is to adopt a personalized decision-making (PDM) method by collecting an

∗First author, U-VR Lab., GIST, Oryong-dong, Buk-gu, Gwangju, South Korea.†Corresponding author, U-VR Lab., GIST, Oryong-dong, Buk-gu, Gwangju, South Korea.

109

http://dx.doi.org/10.1142/S0219622011004245


110 A. Choi & W. Woo

individual user’s physiological data in his/her everyday life. As it would requiremuch time and efforts to collect reliable data during long periods of time, we mustconsider tradeoffs between TDM and PDM methods when designing physiologicalmonitoring systems.

There have been lots of researches on decision-making with data mining method,machine learning method in the health domain for this purpose.4–8 To minimizethe effect of personal differences and to reduce the complexity of signal analysis,Jose proposed a regression model assuming that current physiological states resultfrom previous physiological states which determined the normal heart rate of indi-viduals depending on their age and sex.5 In addition, Miller and Londeree madeformulas for heart rate analysis considering sex.6,7 However, most previous formu-las followed deterministic approach and these methods were adapted to empiricalobservation in a specific task only. Other contextual information such as activityalso has been considered. Wu indicated the physiological decision-making methodwith user’s activity information.9 They inferred users’ activity with Naive Bayesclassifier, and eliminated motion artifact from corrupted physiological signal. Zhangproposed diagnostic decision support model based on yinyang wuxing equilibriumapproach referred by traditional Chinese medicine where he used multiple contex-tual information for diagnosis.8 However, still there is no acceptable formula to beused widely and no satisfactory approaches yet for all users.

To address these issues, we explore a decision-making method to analyze physio-logical signals accurately for different types of people. Our method exploits multiple-group contexts such as age, sex, height, weight, etc., and its relationship. Theirrelationships with physiological signals are formulated using a MAP estimation toobtain ideal expectation of users’ physiological status. MAP estimation has turnedout to be MCDM problem given the assumption that all pdfs follow exponentialforms, especially Gaussian. Each term of MCDM formula corresponds to the effectof group context such as age, sex, height, weight, etc. For analyzing the effective-ness of the proposed method, we collect normal and abnormal data of multipleusers from a PhysioNet database and decide users’ status using TDM, PDM, andMCDM with multiple group contexts.

The proposed method has the following advantages. By referencing similar groupdata distribution, MCDM method estimates users’ physiological status more accu-rately in a short time than TDM method. In other words, it does not require largenumber of individual users’ data; eventually it reduces training time and effortwhile keeping the estimation result approximated to one by using PDM method. Inaddition, the MCDM method has a beneficial effect on various populations becauseit adopts group’s data distribution. It preserves performance constantly regard-less of population of abnormal users. Even though there exist increased popula-tion of abnormal subjects, physiological data distributions of various populationsare reflected in the result of physiological status recognition and we observe theimproved results comparing to one by using TDM method in various cases.


MCDM Based on Probabilistic Estimation for Physiological Signal Monitoring 111

The following section of this paper is as follows. We explain related works inSec. 2 and the proposed analysis method in Sec. 3. Section 4 shows the experientialsetup and analysis results for verifying the proposed method. Finally we concludein Sec. 5 and illustrate the future direction of this research.

2. Related Works

In health, typical decision-making systems use statistical pattern classificationmethods to analyze the physiological signals.4–8 Most previous researchers collecteda large data set from hospitals and found out a set of statistical values (mean, stan-dard deviation, etc.) of healthy and unhealthy people. However, this method maynot cover all users, e.g. people with higher heart rate range than others in normalcondition. To address this problem, Jose explored deterministic analysis method ofabnormal heart rate detection considering age and sex.5 He built a regression modelto differentiate normal range against different personal groups. In addition, Millerand Londeree made formulas for heart rate analysis considering sex.6,7 However,most previous formulas followed deterministic approach, which has less flexibilitysuch that we cannot revise and modify for further analysis.

Other researchers used contextual information such as mood, activity for physi-ological decision-making. Wu discussed the decision-making method based on user’sactivity information by eliminating motion artifact.9 These studies effectively fil-tered motion artifacts, but did not reflect information such as individual differences.These methods were adapted to empirical observations in a specific task and weredesigned to include a single decision criterion such as age, motion artifact, or activ-ity for the analysis. However, we must embrace multiple criteria simultaneously fordecision-making in health.

To deal with multiple criteria, researchers in data mining, management,and machine learning introduced various MCDM methods; utility theory-basedmethod,10,11 knowledge-based method,12,13 fuzzy theory-based method,14,15 andprobabilistic model-based method.16–18 Most commonly referred methods areutility-based and knowledge-based methods.10–12 Torrance and Huber proposeda multiattribute utility function for health states classification, applying weightsfor decision-making based on empirical observation.10,11 However, it is hard todefine utility function because there is too little background theory to indicatefactors which influence the physiological signals and its relationships. Therefore,some researchers suggested the decision-making method, appropriate to deal withuncertainty problem of physiological signal analysis as well as to make it in gen-eral.14–18 Carlsson and Rao introduced fuzzy theory-based DM methods whichsupported uncertain reasoning under the vagueness phenomenon. However, thismethod requires novel knowledge to define fuzzy rule for analyzing personaldifferences. Unlike the above methods, probabilistic methods have advantages todeal with dependency between criteria.16–18 Thus, we explore the way to model



decision-making probabilistically and by referring to previous works about groupingmethod.19

3. Multiple-Criteria Decision-Making Based on a Group Context

In this section, we explore a MCDM method derived from MAP estimation forphysiological signal analysis. Physiological analysis without considering personaldifferences increase the risen misdiagnosis. For example, a person who has highheart rate in normal condition may be misdiagnosed for a heart problem. There-fore, decision-making based on contextual information needs to be improved withmore accurate analysis of sensing conditions and users’ normal or abnormal con-ditions. However, we have little information to determine which factors influencephysiological signal, and how much the factors are affected. Therefore, we appliedprobability theory for problem formation. Research on decision-making algorithmsaddressed uncertainty of influencing factors.17,18 Because of the uncertainty, rela-tionships between variables are modeled with conditional probabilities based onBayes’ theorem.16

The proposed decision-making method has the following procedure as shown inFig. 1. For preprocessing of collected data, we extract features from original signalsand segment certain periods of time for consistent and reliable analysis. Then,selected features are filtered by smoothing and removing third order trends. Indecision-making step, we estimate a density function from the physiological signaldatabase. Since there are numerous density estimation methods, we first check theKolmogorov–Smirnov tests to verify the normality of the collected data. Then MAPestimation is processed based on filtered signal and estimated density function. Afterfinding ideal data distribution, we determine whether current condition of a subjectwas normal or abnormal by several thresholds such as an individual threshold, agroup threshold, and a general standard threshold.

For the MAP estimation, we formulate the problem as follows. First, we assumethat the data distribution and error follow a Gaussian probability density func-tion because most physiological measurements are in the middle range. It indicates

Fig. 1. Overall procedure of physiological signal decision-making.



that physiological measurement has higher probability to observe normal statussubjects rather than abnormal subjects. We abbreviate the observed physiologi-cal data d following a Gaussian probability density function and the user physio-logical states u of observed data following Gaussian probability density function.M = {m1, m2, m3, . . . , mp} is the model for groups (e.g. male, female) where p isthe number of models. T = {t1, t2, t3, . . . , tn} refers to the type of user status (e.g.normal, abnormal), and n to the number of types. To find the ideal user physiolog-ical states u, we apply the MAP estimation method. To maximize the probabilityof the current user status, we apply the following equation:

u∗ = argmaxu

P (u|d, m, t) = arg maxu

P (u,d,m,t)P (d,m,t)

∝ argmaxu

P (u, d, m, t)(3.1)

We assume that u is derived from the conditional probability given observationd, other group reference model m, and user states t. In Eq. (3.1), we ignore P (d, m, t)because probability function in terms of d, m, t does not involve information aboutu ideal expectation. Therefore, we find the original MAP estimation in proportionto the joint probability of u, d, m, and t.

To simplify Eq. (3.2), we decompose the joint probability through a data-observation process, group-observation process, and status-decision process. In thedata observation process, the observation data d is estimated from the given groupdistribution m, status information t, and expected distribution u. For the group-observation process, the group distribution is computed according to the type t andideal expectation u. We derive the final status type from the expected distribution.

P (u, d, m, t) = P (d|u, m, t) ∗ P (u, m, t)

= P (d|u, m, t) ∗P (u,m,t)

︷︸︸︷

P (m|u, t) ∗ P (u, t)

= P (d|u, m, t) ∗ P (m|u, t) ∗P (u,t)

︷︸︸︷

P (t|u) ∗ P (u) (3.2)

As a result, we factorize the multivariable joint probability function into severalsimple conditional probability functions given one or two variables (3.2). To com-pute each term of joint probability, we begin with some notations. If we assume thateach joint pdf follows Gaussian distribution, f(u; θ), we denote potential functionsassociated with exponential form, where

f(u; θ) ∝ e−〈θ,φ(u)〉 (3.3)

Note that θ is a real-valued vector, known as Gaussian parameter and φ(u) ispotential energy equation indicating distance between real-valued observation andexpectation. From (3.3) and (3.2), MAP estimation in this case becomes an energyminimization problem (3.4) and turns out a MCDM problem given the assumption



that all pdfs follow exponential forms, especially Gaussian.

u∗ = arg maxu

P (u, d, m, t)

= arg maxu

[P (d|u, m, t) × P (m|u, t) × P (t|u) × P (u)]

= arg maxu

[e−〈θd,φ1(u,m,t)〉 × e−〈θm,φ2(u,t)〉 × e−〈θt,φ3(u)〉 × e−〈θu,φ4(u)〉]

= arg maxu

[e−(〈θd,φ1(u,m,t)〉+〈θm,φ2(u,t)〉+〈θt,φ3(u)〉+〈θu,φ4(u)〉)]

= arg minu

[〈θd, φ1(u, m, t)〉 + 〈θm, φ2(u, t)〉 + 〈θt, φ3(u)〉 + 〈θu, φ4(u)〉]. (3.4)

We define that e1 is an energy function of P (d|u, m, t) from the differencebetween the observed data and the group distribution, e2 is an energy functionof P (m|u, t) from the difference between the group distribution and ideal distribu-tion, and e3 is an energy function of P (t|u) representing the difference between thestatus t and the ideal estimation u. Assuming that P (t|u) is constant (p = 0.5), e3

equals zero. e1, e2, and e3 are represented as follows:

e1 = ‖θd − φ1(u, m, t)‖2, e2 = ‖θm − φ2(u, t)‖2, e3 = ‖θt − φ3(u)‖2 (3.5)

After estimating the ideal distribution of the observation, we determine whetherthe condition of a user is normal or not. For the recognition, we apply differentthresholds calculated by group distribution labeled with group context. For exam-ple, if we have an age-group database, we categorize the data according to individualusers’ current physiological status (e.g. normal or abnormal), obtaining four groupmodels: normal male, abnormal male, normal female, and abnormal female. Weset a threshold at the intersection point of the normal male group distribution andabnormal male group distribution, and it figures out the current users’ physiologicalstatus according to it.

4. Experimental Analysis

We evaluated our MCDM method with real data set based on heart rate of healthyor unhealthy subjects. We used the normal sinus rhythm RR interval databaseto identify normal sinus rhythm data and the congestive heart failure RR inter-val database to identify tachycardia sinus rhythm in PhysioBank.20 Tachycardia istypically defined by excessive heart rate at rest. We associated users with tachy-cardia sinus rhythm to an abnormal condition. We collected the heart rate data of54 normal subjects from the normal sinus rhythm RR interval database: 30 malesaged 28.5–76; 24 females aged 58–73. We collected data about 18 subjects aged34–79 from the congestive heart failure RR interval database (NYHA classes III)including 9 abnormal subjects and 9 normal subjects.

We extracted features from heart rate and selected 5-min long RR samples foreach subject. We processed the measurements to correct artifacts smothing and toremove third order trends in RR intervals. Then, we computed feature from the



RR intervals to compute heart rate, because this factor characterizes signals in thetime domain. We estimated a density function to discriminate the normal fromabnormal conditions. Since density estimation methods are numerous, we verifiedthe normality of the collected data with Kolmogorov–Smirnov tests. Finally, weobtained a probability density function about each data set.

We determined whether the current condition of a subject was normal or abnor-mal with an individual threshold, a group threshold, and a general standard thresh-old. We fixed the standard threshold at 100 bpm because we just collected fast heartbeat condition of abnormal subjects. For the group threshold, we categorized thesubjects based on sex and age. The two sex groups were labeled male and female. Wedefined three age groups: 20–39, 40–59, and 60–79 years old. Individual thresholdswere computed from individual distributions following 95% certification interval ofeach density distribution.

Overall classification errors thanks to group contexts decreased as shown inFig. 2. The standard threshold (under 100 bpm) significantly reduced classificationerrors in the case of normal subjects group. But, subjects with tachycardia sinusrhythm were often misclassified. However, our method exploiting age–sex contextskept the low error rates for all subjects, as shown in Fig. 2. Average error rates inPDM method, proposed method with group context: age–sex, age only, sex only,and TDM method were 5% (PDM), 7.33% (age–sex), 12.59% (age only), 15.09%(sex only), and 27.75 % (TDM), respectively. We concluded that our method withage–sex contexts affects more positively than the other deterministic and TDMmethods. Besides, the classification increasingly succeeded with additional contex-tual information. For instance, the overall classification better succeeds with age–sex than with age only. As a result, our method considering group context reducedclassification errors by 20.42% when compared to TDM methods.

Normal Subjects Abnormal Subjects0

20

40

60

80

100

Cla

ssifi

catio

n E

rror

(%

)

PDM

TDM

MCDM (Sex)

MCDM (Age)

MCDM (Age-Sex)

Fig. 2. Heart rate classification results of TDM, MCDM with context and PDM methods.



(a) (b)

Fig. 3. Data distribution by sex group. (a) Male group (normal subject = 70%, abnormal subject =30%). (b) Female group (normal subject = 70%, abnormal subject = 30%).

w/ocontext

wcontext

w/ocontext

wcontext

Male Female

Cas

sifi

cati

on

Err

or(

%)

Type 1 Error

Type 2 Error

0

20

40

60

80

100

(a) (b)

Fig. 4. Classification result by sex group. (a) Definition of type of error. (b) Classification result(normal subject = 70%, abnormal subject = 30%).

We analyzed the error type of classification by clarifying which errors increasedor deduced for different thresholds. The classification result is illustrated inFigs. 3–5. Figures 3(a) and 3(b) indicate the distribution of each sex group witha population consisting of 50% normal and 50% abnormal subjects. We checkedfor Type 1 error and Type 2 error in each distribution as detailed in Fig. 4(a). AType 1 error is defined by the identification of an unhealthy subject as healthy; AType 2 error is the opposite. As shown in Fig. 4(b), the classification ratio dimin-ishes when we apply a sex group threshold to decide the health status, assuming50% of participation are abnormal.

In addition, our grouping analysis with age context exhibits fewer errors than aTDM method, as shown in Fig. 5. In both cases, Type 1 errors decrease dramaticallybut Type 2 errors do not. The TDM method extends the possibility to detectnormal subjects. From this experiment, we also conclude that our method betterclassifies people with an age context than with a sex context. The classification



(a) (b)

0

20

20-39 40-59 60-79

40

60

80

100C

lass

ific

atio

nE

rro

r (%

)Type 1 Error

Type 2 Error

w/o w w/o w/o ww

(c) (d)

Fig. 5. Classification result by age group. (a) Distribution for 20–39 age group (normal subject =70%, abnormal subject = 30%). (b) Distribution for 40–59 age group (normal subject = 70%,abnormal subject = 30%). (c) Distribution for 60–79 age group (normal subject = 70%, abnormalsubject = 30%). (d) Classification result (normal subject = 70%, abnormal subject = 30%), where“w/o” is without context, “w” is with context.

errors are reduced by a group-based MCDM method as well as by a PDM method.Accordingly, age and sex contexts, especially age, can improve the estimation of theuser status without knowledge of his/her data distribution. However, it is hard toget benefit using MCDM method in the case of sex group classification, especiallyfemale group, because the collected data is broadly distributed.

In addition, we compared the classification results for different prevalences ofunhealthy subjects as shown in Figs. 6 and 7. We tested for three population profiles:50%, 70%, and 90% in normal. Overall context improved classification results. Fora portion of abnormal subjects reaching 50% in 60–79 age group, the classificationrate improves by 31.59%, in most cases, errors with the TDM method along with theproportion of abnormal users. The MCDM method performs constantly, regardlessof the proportion of abnormal users. Our method considered normal subjects aswell as abnormal subjects; thus, it indicated good classification ratio to increased



2

4

6

8

10

0

0

0

0

0

0Cla

ssif

icat

ion

Err

or

(%)

Population ratio(% of Normal users/ % of Abnormal users)

Threshold w/o context

Threshold w context

7.1818.50

29.82

5.69 5.67 6.25

90% / 10% 70% / 30% 50% / 50%

Cla

ssif

icat

ion

Err

or

(%)

100

Threshold w/o context80

Threshold w context

41.8560

19.9630.91

30 40 35.36

40

13.87

30.40

0

20

13.870

90% / 10% 70% / 30% 50% / 50%Population ratio

(% of Normal users/ % of Abnormal users)

(a) (b)

Fig. 6. Classification result by sex group with population. (a) Male group. (b) Female group.

Cla

ssif

icat

ion

Err

or

(%)

6.50 11.07 11.59

20.6613.58

6.50

100

60

80

40

60

20

40

0



Threshold w context

90% / 10% 70% / 30% 50% / 50%

Cla

ssif

icat

ion

Err

or

(%)


100Threshold w/o context

80Threshold w context

60

13 46

40

2.908.18

13.46

0

20

1.71 2.43 2.350

90% / 10% 70% / 30% 50% / 50%

(a) (b)

Cla

ssif

icat

ion

Err

or

(%)


Threshold w context

90% / 10% 70% / 30% 50% / 50%

80

100

60

80

40

60

20

00.68

6.9720.91

34.84

1.92 3.25


(c)

Fig. 7. Classification result by age group with population. (a) 20–39 age group. (b) 40–59 agegroup. (c) 60–79 age group.

abnormal population. Especially, the analysis result in 60–79 age group and malegroup indicated greater improvement rather than the other group. Female group,20–39 aged group showed little effects on using contextual information becausefemale groups’ distribution of collected data is widely distributed; thus, it is hardto characterize the data features of that group.



5. Conclusions and Future Works

We proposed a MCDM method for physiological signal analysis and tested theseideas with a public physiological data set. The problem was formulated using MAPestimation for obtaining ideal expectation of users’ physiological status. MAP esti-mation eventually was rearranged by MCDM problem given the assumption thatall pdfs followed exponential forms, especially Gaussian. From the experiment con-ducted, we achieved 20.42% improvement of physiological status classification byapplying the MCDM method with age–sex group context than TDM methods.Furthermore, MCDM method with various populations also produced better clas-sification results than TDM method. If a portion of abnormal subjects of age groupreached from 10% to 50%, classification rate was improved by 6.29% and 31.59%,respectively.

In future studies, we will consider external variables such as air temperature andhumidity in addition to internal variables. We expect such contextual informationto improve normal physiological status. These additions will support the creationsituation of a model to estimate in diverse situations. Finally, we expect that thiswork is applicable to various personalized physiological signal monitoring applica-tions, especially daily health monitoring in which we easily collect several sensorydata from heterogeneous resources. In this environment, system estimates user’sphysiological status by referring other group distribution without prior knowledgeabout previous health records in real time.

Acknowledgments

This research is supported by Ministry of Culture, Sports and Tourism (MCST)and Korea Creative Content Agency (KOCCA), under the Culture Technology(CT) Research & Development Program 2010.

References

1. H. H. Asada, H. H. Jiang and P. Gibbs, Active noise cancellation using MEMSaccelerometers for motion tolerant wearable bio-sensors, in Proc. 26th Int. Conf. IEEEEngineering in Medicine and Biology Society, eds. D. L. Hudson, Z. P. Liang andG. Dumont (San Francisco, California, 2004), pp. 2157–2160.

2. R. Matthews, N. J. McDonald, P. Hervieux, P. J. Turner and M. A. Steindorf, Awearable physiological sensor suite for unobtrusive monitoring of physiological andcognitive state, in Proc. 29th Int. Conf. IEEE Engineering in Medicine and BiologySociety, eds. J. Rousseau, G. Delhomme and M. Akay (Lyon, France, 2007), pp. 5276–5281.

3. U. Anliker, J. A. Ward, P. Lukowicz, G. Troster, F. Dolveck, M. Baer, F. Keita,E. B. Schenker, F. Catarsi, L. Coluccini, A. Belardinelli, D. Shklarski, M. Alon,E. Hirt, R. Schmid and M. Vuskovic, AMON: A wearable multiparameter medi-cal monitoring and alert system, IEEE T. Inf. Technol. Biomed. 8 (2004) 415–427,doi:10.1109/TITB.2004.837888.

4. R. A. Miller, Medical diagnostic decision support systems–past, present and future: Athreaded bibliography and brief commentary, J. Am. Med. Inf. Assoc. 1 (1994) 8–27,doi:10.1136/jamia.1994.95236141.



5. A. D. Jose and D. Collison, The normal range and determinants of the intrinsic heartrate in man, Cardiovasc. Res. 4 (1970) 160–167, doi:10.1093/cvr/4.2.160.

6. B. R. Londeree and M. L. Moeschberger, Effect of age and other factors on HR max,Res. Q. Exerc. Sport 53 (1982) 297–304.

7. W. C. Miller, J. P. Wallace and K. E. Eggert, Predicting max HR and the HR-[latincapital V with dot above]2 relationship for exercise prescription in obesity, Med. Sci.Sports Exerc. 25 (1993) 1077–1081.

8. W. R. Zhang and S. S. Chen, Equilibrium and nonequilibrium modeling of yinyangwuxing for diagnostic decision support in traditional Chinese medicine, Int. J. Inf.Technol. Decision Making 8 (2009) 529–548, doi:10.1142/S0219622009003521.

9. W. H. Wu, M. A. Batalin, L. K. Au, A. A. T. Bui and W. J. Kaiser, Context-awaresensing of physiological signals, in Proc. 29th Int. Conf. IEEE Engineering in Medicineand Biology Society, eds. J. Rousseau, G. Delhomme and M. Akay (Lyon, France,2007), pp. 5271–5275.

10. G. W. Torrance, D. H. Feeny, W. J. Furlong, R. D. Barr, Y. Whang and Q. Wang,Multiattribute utility function for a comprehensive health status classification system:Health utilities index mark 2, Med. Care 34 (1996) 702–722, doi:10.1097/00005650-199607000-00004.

11. G. P. Huber, Multi-attribute utility models: A review of field and field-like studies,Manage. Sci. 20 (1974) 1393–1402, doi:10.1287/mnsc.20.10.1393.

12. Y. Peng, G. Kou, Y. Shi and Z. Chen, A descriptive framework for the field of datamining and knowledge discovery, Int. J. Inf. Technol. Decision Making 7 (2008) 639–682, doi:10.1142/S0219622008003204.

13. D. J. Hall and R. A. Davis, Engaging multiple perspectives: A value-baseddecision-making model, Decision Supp. Syst. 43 (2007) 1588–1604, doi:10.1016/j.dss.2006.03.004.

14. C. Carlsson and R. Fuller, Fuzzy multiple criteria decision making: Recent develop-ments, Fuzzy Sets Syst. 78 (1996) 139–153, doi:10.1016/0165-0114(95)00165-4.

15. C. Rao and J. Peng, Fuzzy group decision making model based on credibility theoryand gray relative degree, Int. J. Inf. Technol. Decision Making 8 (2009) 515–527,doi:10.1142/S0219622009003533.

16. G. Parmigiani, Modeling in Medical Decision Making: A Bayesian Approach (Wiley,London, 2002).

17. M. Ozturk and A. Tsoukias, Modeling uncertain positive and negative reasons in deci-sion aiding, Decision Supp. Syst. 43 (2007) 1512–1526, doi:10.1016/j.dss.2006.06.005.

18. H. Eskandari and L. Rabelo, Handling uncertainty in the analytic hierarchy pro-cess: a stochastic approach, Int. J. Inf. Technol. Decision Making 6 (2007) 177–189,doi:10.1142/S0219622007002356.

19. H. K. Alfares and S. O. Duffuaa, Determining aggregate criteria weights from criteriarankings by a group of decision makers, Int. J. Inf. Technol. Decision Making 7 (2008)769–781, doi:10.1142/S0219622008003174.

20. A. L. Goldberger, L. A. N. Amaral, L. Glass, J. M. Hausdorff, P. C. Ivanov, R.G. Mark, J. E. Mietus, G. B. Moody, C. K. Peng and H. E. Stanley, PhysioBank,PhysioToolkit and PhysioNet: Components of a new research resource for complexphysiologic signals, Circulation 101 (2000) e215–e220.

Documents

January 11, 2011 8:58 WSPC/S0219-6220 173-IJITDM …icserv.gist.ac.kr/mis/publications/data/2011/S... · · 2011-01-19January 11, 2011 8:58 WSPC/S0219-6220 173-IJITDM 00424 International